CONSIDERABLE EFFORT HAS GONE INTO DEVELOPING THE BASIC QUANTITATIVE THEORY FOR COMPARTMENTAL SYSTEMS WITH TIME LAGS, FOR LINEAR AND FOR NONLINEAR COMPARTMENTAL SYSTEMS. WE HAVE SHOWN THAT THERE IS A BROAD CLASS OF COMPARTMENTAL SYSTEMS WITH LAGS FOR WHICH THE DISTRIBUTION FUNCTIONS FOR CONTINUOUS LAG DISTRIBUTIONS ARE THEMSELVES GENERATED BY COMPARTMENTAL SYSTEMS WITHOUT LAGS. FOR SUCH SYSTEMS, THE GENERAL THEORY IS THE SAME AS THAT FOR SYSTEMS WITH LAGS. [JACQUEZ, JA AND CP SIMON. SIAM REV. 35:43-79, 1993]. WORK CONTINUED ON THIS PROJECT IN THE CURRENT YEAR, AND WAS PRESENTED AT A CONFERENCE ON DIFFERENTIAL EQUATIONS HELD IN CLAREMONT, CA IN JUNE, 1995.